Volume of Truncated Icosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
V = 5*((2*rm)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Volume of Truncated Icosidodecahedron - (Measured in Cubic Meter) - Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.
Midsphere Radius of Truncated Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Icosidodecahedron is the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Truncated Icosidodecahedron: 37 Meter --> 37 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 5*((2*rm)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))) --> 5*((2*37)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
Evaluating ... ...
V = 195593.343876297
STEP 3: Convert Result to Output's Unit
195593.343876297 Cubic Meter --> No Conversion Required
FINAL ANSWER
195593.343876297 195593.3 Cubic Meter <-- Volume of Truncated Icosidodecahedron
(Calculation completed in 00.004 seconds)

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5 Volume of Truncated Icosidodecahedron Calculators

Volume of Truncated Icosidodecahedron given Total Surface Area
Go Volume of Truncated Icosidodecahedron = 5*(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))^3)*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron given Surface to Volume Ratio
Go Volume of Truncated Icosidodecahedron = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron given Circumsphere Radius
Go Volume of Truncated Icosidodecahedron = 5*((2*Circumsphere Radius of Truncated Icosidodecahedron)/(sqrt(31+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron given Midsphere Radius
Go Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron
Go Volume of Truncated Icosidodecahedron = 5*Edge Length of Truncated Icosidodecahedron^3*(19+(10*sqrt(5)))

Volume of Truncated Icosidodecahedron given Midsphere Radius Formula

Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
V = 5*((2*rm)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))

What is a Truncated Icosidodecahedron?

In geometry, the Truncated Icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. It has 62 faces which include 30 squares, 20 regular hexagons and 12 regular decagons. Each vertex is identical in such a way that, one square, one hexagon and one decagon join at each vertex. It has the most edges and vertices of all Platonic and Archimedean solids, though the snub dodecahedron has more number of faces. Out of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the Snub Dodecahedron (89.63%) and Small Rhombicosidodecahedron (89.23%), and less narrowly beating the Truncated Icosahedron (86.74%).

How to Calculate Volume of Truncated Icosidodecahedron given Midsphere Radius?

Volume of Truncated Icosidodecahedron given Midsphere Radius calculator uses Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))) to calculate the Volume of Truncated Icosidodecahedron, Volume of Truncated Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the midsphere radius of the Truncated Icosidodecahedron. Volume of Truncated Icosidodecahedron is denoted by V symbol.

How to calculate Volume of Truncated Icosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Truncated Icosidodecahedron given Midsphere Radius, enter Midsphere Radius of Truncated Icosidodecahedron (rm) and hit the calculate button. Here is how the Volume of Truncated Icosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 195593.3 = 5*((2*37)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))).

FAQ

What is Volume of Truncated Icosidodecahedron given Midsphere Radius?
Volume of Truncated Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the midsphere radius of the Truncated Icosidodecahedron and is represented as V = 5*((2*rm)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))) or Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))). Midsphere Radius of Truncated Icosidodecahedron is the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere.
How to calculate Volume of Truncated Icosidodecahedron given Midsphere Radius?
Volume of Truncated Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the midsphere radius of the Truncated Icosidodecahedron is calculated using Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5))). To calculate Volume of Truncated Icosidodecahedron given Midsphere Radius, you need Midsphere Radius of Truncated Icosidodecahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius of Truncated Icosidodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Volume of Truncated Icosidodecahedron?
In this formula, Volume of Truncated Icosidodecahedron uses Midsphere Radius of Truncated Icosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Volume of Truncated Icosidodecahedron = 5*Edge Length of Truncated Icosidodecahedron^3*(19+(10*sqrt(5)))
  • Volume of Truncated Icosidodecahedron = 5*(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))^3)*(19+(10*sqrt(5)))
  • Volume of Truncated Icosidodecahedron = 5*((2*Circumsphere Radius of Truncated Icosidodecahedron)/(sqrt(31+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))
  • Volume of Truncated Icosidodecahedron = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5)))
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